The limit as x approaches 36 for the expression (√x - 6) / (x - 36) requires careful handling due to the denominator equating to zero at that point. Direct substitution is not viable, leading to the necessity of rationalizing the numerator. By multiplying both the numerator and denominator by (√x + 6), the limit can be simplified and evaluated effectively, resulting in a defined value.
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Jan Hill said:Homework Statement
How do you solve the following the limit as x approaches 36 of numerator = (square root of x) - 6 and numerator x - 36Homework Equations
The Attempt at a Solution
We can't just substitute in x = 36 because then the denominator will be 0 and the expression will be undefined. Do we multiply by the reciprocal of the numerator?